General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions (1401.1579v1)

Abstract: We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of three-coupled nonlinear Schr\"odinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between one-dimensional long-wave and multiple short-waves. The Painlev\'e analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative and mixed nonlinearity coefficients. We obtain general bright $N$-soliton solution of multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark and grey types, when the long-wave--short-wave resonance takes place. The short-wave component solitons undergo two types of energy sharing collisions. The solitons appearing in the long-wave component always exhibit elastic collision whereas that of short-wave components exhibit standard elastic collisions only for specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pair-wise nature of collision and unravel fascinating state restoration property.